FRACTIONAL FOURIER-TRANSFORM APPLIED TO SPATIAL-FILTERING IN THE FRESNEL DOMAIN

The fractional Fourier transform can be optically defined through a phase-space coordinate rotation of the Wigner distribution function associated with the input signal. This operation can be achieved by performing three successive shearing processes, which are reduced to a free-space Fresnel diffraction originated by a scaled version of the input object illuminated with a spherical wave. This result is applied to describe the behavior of spatial filtering devices based on the self-imaging phenomenon (Fresnel spatial filters).